There is an emerging interest in very high speed machines, having speeds in the range of 20,000 to 60,000 revolutions per minute (rpm), for use in appliances, aerospace, and other applications. The foremost features that are required for these machines are high efficiency and low acoustic noise. For high efficiency operation of these machines, it is important to examine the dominant effects of each and every loss in the machine. There are three dominant losses to be considered in these machines that impose significant design and operational constraints. These dominant losses are: (1) copper or resistive losses, (2) core losses, and (3) frictional and winding losses.
Copper or resistive losses result from the flow of current in the stator windings. The windings invariably have resistances, and currents in them produce a voltage drop, v, equal to the current, i, times the resistance, R, expressed as v=Ri. Since a current is flowing through the resistive element, the voltage drop produces a power loss, p, across the windings equal to the current times the voltage drop, which, in turn, equals the resistance times the square of the current, which is expressed as p=vi=i2R. For a given power, if the current is minimized, then the only parameter to impact the resistive power loss is its resistance.
The resistance for a given winding varies with its temperature and a skin effect. Temperature sensitivity is determined by a physical coefficient of the winding material and the temperature rise in the windings due to their excitation. The temperature rise can be controlled by a cooling arrangement, and its upper limit is determined by the thermal capability of the winding's insulator material. Therefore, there is not much that can be done to reduce the resistive losses beyond optimizing the winding material and its cooling arrangement.
The skin effect is due to the frequency of the current that is flowing in the winding and is controlled by the phase switching frequency (PSF), which is different from the pulse width modulation (PWM) frequency. The PSF is determined by how many times a phase experiences current per unit time (i.e., a second) and is determined by the number of poles of the switched reluctance machine (SRM). Therefore, the PSF can be minimized by minimizing the number of poles and operating the machine at lower speed. While the pole numbers can be minimized, the upper speed limit is not determined by the machine but by the application, and, hence, the upper speed (i.e., the highest speed that the machine will experience) is a dominating factor in the machine design.
In the final analysis, it can be deduced that the resistive losses are determined by: (a) temperature sensitivity of the winding material and (b) frequency of the alternating current (ac) component of the current, primarily that of the phase switching frequency. The frequency of the current's ac component is determined by the number of poles of the rotor and stator and by the upper speed of the machine, which is determined by the application and not by anything one can do in the machine design. Therefore, the upper speed of the machine is an independent variable. The temperature sensitivity of the winding material, the frequency of the ac component, and the number of rotor and stator poles can, however, be controlled by the machine designer, within the constraints of the physical characteristics of materials and the necessary pole numbers. Therefore, the resistive losses can be minimized to an extent.
Besides resistive losses, core losses constitute another type of the dominant losses affecting TPSRM design. The core material of a TPSRM experiences a loss due to the varying flux flow in it. The core losses consist of two parts, hysteresis loss and eddy current loss. The hysteresis loss is influenced by the frequency of the flux and flux density in the material and a physical factor of the material. The frequency of the flux is determined by the phase switching frequency, which in turn is determined by the upper speed of the machine. Assuming that flux density is kept at a desired level to generate the required torque, then the factor that is under the control of the designer is the phase switching frequency, but only to an extent as explained above.
Eddy current loss is due to the flow of eddy currents in the laminations and is a function of the square of the frequency and the square of the flux density, as well as other variables, such as the square of the thickness of the lamination material. The thickness of the lamination materials is determined primarily by the cost, and, hence, it is prefixed for each and every application. Therefore, to minimize the eddy current loss, the designer has to minimize the flux density and phase switching frequency.
From the above discussion, it may be seen that is important to reduce the frequency of the phase flux and the magnitude of flux density in the material, to minimize core losses.
The third type of dominant loss affecting TPSRM design is friction and winding loss. This type of loss is a function of the rotor and stator pole shapes and the air gap between them. Given an electromagnetic design of the stator and rotor pole shapes, there is not much that can be done to reduce the friction and winding losses, other than filling the rotor interpolar space with a magnetically inert material, so that the rotor is cylindrical. Also, the stator may be constructed with a thermally-conducting, but magnetically inert, material between the coils of each pole and its adjacent pole, so the stator's inner surface is full of material with no gap other than the air gap in its vicinity. But this is a cost issue, and, therefore, it may not be possible for all applications, particularly for low-cost applications, such as in home appliances.
From the above discussion of the various machine losses, it may be discerned that it is important to minimize all the core loss components, but most importantly the ones that will dominate in the final analysis, related to electromagnetics in very high speed machines. These components can be minimized by controlling the flux density and also by minimizing the frequency of the flux in the materials. Once the pole numbers and upper speed are fixed, the frequency of the flux is also fixed. Thereafter, the design variables available to the designer for minimizing core losses are few or nonexistent. Examining very closely the core losses for various parts of the machine, such as the stator and rotor poles and the stator and rotor back irons, a degree of freedom in tackling the core losses becomes evident. That is, the designer can minimize the core losses in each and every part separately. The core losses for these parts are described below.
The stator and rotor back irons usually have bipolar flux in most SRM machines and experience flux reversals. In the stator poles, the flux density should be maximized for a minimum of material weight. Stator poles do not experience flux reversals. The flux in the rotor poles is also bipolar and designed not to exceed the maximum peak flux density of the materials.
FIG. 1 illustrates a related art TPSRM having 4 stator poles and 2 rotor poles (a 4/2 stator/rotor pole combination) and the machine's flux paths when phase A is excited. FIG. 2 illustrates the TPSRM of FIG. 1 and its flux paths when phase B is excited. Phase A consists of windings 101 and 102 on diametrically opposite stator poles 105 and 106 connected in series, though they could alternatively be connected in parallel. Likewise, phase B consists of series (or parallel) connected windings 103 and 104 on diametrically opposite stator poles 107 and 108. The flux paths for phase A's stator poles 105 and 106, when excited and aligned with rotor poles 109 and 110, are identified by reference characters 111 and 112. Similarly, the flux paths for phase B's stator poles 107 and 108, when excited and aligned with rotor poles 109 and 110, are identified by reference characters 113 and 114. As may be determined by inspection of FIGS. 1 and 2, stator poles 105-108 do not experience flux reversal for unidirectional current excitation of phases A and B. However, rotor poles 109 and 110 do experience flux reversal as they move from one stator pole (say phase A's) to another stator pole having the same phase. Likewise, rotor back iron 115, which includes the regions between rotor poles 109 and 110 and around shaft 116, also undergoes flux reversal. Similarly, stator back iron segments 117 and 119 experience flux reversal. Stator back iron segment 117 is located in the region between stator poles 105 and 108, stator back iron segment 118 is located in the region between stator poles 106 and 108, stator back iron segment 119 is located between stator poles 106 and 107, and stator back iron segment 120 is located between stator poles 105 and 107.
The above-described flux reversals create: (i) forces in the opposite direction for each flux reversal, thereby causing stator acceleration and, hence, higher acoustic noise generation; and (ii) increased core losses.